There is a different approach to obtain Hölder continuity for degenerate equations using expansion of positivity, see [1]}.
The main feature of this method is that neither the logarithmic integral estimate nor the analysis of two alternatives in the key steps of the original proof are needed.
The expansion of positivity is a fundamental ingredient in proving a Harnack inequality, see [2]}.
We refrain from using these techniques so that our proof stays self-contained.
Furthermore, it is also not clear whether this approach allows for the reaction term we are considering.
